#2033 ⟨
a
,
b
,
c
|
aaaa
=1,
abac
=1⟩
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Monoid enumeration
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#2032
⟨
a
,
b
,
c
|
aaaa
=1,
aabc
=1⟩
Next:
#2034
⟨
a
,
b
,
c
|
aaaa
=1,
abbc
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-commutative monoid
Element
ab
a
2
has infinite order
Rewriting system
Format:
Pretty
Plain
Word:
Enter a word above to compute its normal form. Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Strategy:
Leftmost
Rightmost
Result:
1
1
Reduction order:
Left-to-right shortlex with
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
bac
⇒
a
3
[3]
2.
a
4
⇒ 1
[1]
# abc:aaaa=1,abac=1 abc - - bac=aaa aaaa=1